The Associated* groups are the OOTB Visitors, Members, and Owners groups.
You can read more about this here: AssociatedOwnerGroup in SharePoint
Every Site has 3 Site Groups that are associated Site Groups: Visitors (AssociatedVisitorsGroup), Members (AssociatedMemberGroup) and Owners(AssociatedOwnerGroup).
It doesn't appear that there would be any catastrophic changes in MSFT code if you change this, but as a best practice you shouldn't rely on this group existing as it could have been deleted. That post mentions this as well:
If the the association of these 3 groups is not there then if you check programmatically for the AssociatedOwnerGroup property of the SPWeb it would not return any results and your code might fail...
I would assume the properties are there to give developers a (semi-)reliable place to grab groups from in a simple security set up. Using Telerik's JustDecompile the only places these properties are used, it checks if the value is null. It uses the properties to automatically propagate the groups when you create a new site with inherited permissions, if there is no owner's group set, the site permissions are only accessible to the site owner, etc. But there wouldn't be any catastrophic effects to reassigning this or setting it to null.
Here is the output from Telerik's JustDecompile:
(It's hard to see, but if you right click and view image you get the full sized image.)